Overview
- Group
- SmallGroup(560,160)
- Rank
- 3
- Schläfli Type
- {4,70}
- Vertices, edges, …
- 4, 140, 70
- Order of s0s1s2
- 140
- Order of s0s1s2s1
- 2
- Also known as
- {4,70|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
7-fold
10-fold
14-fold
20-fold
28-fold
35-fold
70-fold
Covers minimal covers in bold
2-fold
3-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140);; s1 := ( 1, 71)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 99)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 92)( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,134)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,127)( 51,133)( 52,132)( 53,131)( 54,130)( 55,129)( 56,128)( 57,120)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,113)( 65,119)( 66,118)( 67,117)( 68,116)( 69,115)( 70,114);; s2 := ( 1, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 15, 30)( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)( 24, 28)( 25, 27)( 36, 44)( 37, 43)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 50, 65)( 51, 64)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)( 57, 58)( 59, 63)( 60, 62)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92, 93)( 94, 98)( 95, 97)(106,114)(107,113)(108,119)(109,118)(110,117)(111,116)(112,115)(120,135)(121,134)(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)(130,132);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(140)!( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140); s1 := Sym(140)!( 1, 71)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 99)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 92)( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22, 85)( 23, 91)( 24, 90)( 25, 89)( 26, 88)( 27, 87)( 28, 86)( 29, 78)( 30, 84)( 31, 83)( 32, 82)( 33, 81)( 34, 80)( 35, 79)( 36,106)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,107)( 43,134)( 44,140)( 45,139)( 46,138)( 47,137)( 48,136)( 49,135)( 50,127)( 51,133)( 52,132)( 53,131)( 54,130)( 55,129)( 56,128)( 57,120)( 58,126)( 59,125)( 60,124)( 61,123)( 62,122)( 63,121)( 64,113)( 65,119)( 66,118)( 67,117)( 68,116)( 69,115)( 70,114); s2 := Sym(140)!( 1, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 15, 30)( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)( 24, 28)( 25, 27)( 36, 44)( 37, 43)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)( 50, 65)( 51, 64)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)( 57, 58)( 59, 63)( 60, 62)( 71, 79)( 72, 78)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 85,100)( 86, 99)( 87,105)( 88,104)( 89,103)( 90,102)( 91,101)( 92, 93)( 94, 98)( 95, 97)(106,114)(107,113)(108,119)(109,118)(110,117)(111,116)(112,115)(120,135)(121,134)(122,140)(123,139)(124,138)(125,137)(126,136)(127,128)(129,133)(130,132); poly := sub<Sym(140)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.